IX: 14, 318-335, LNM 465 (1975)
FERNIQUE, Xavier
Des résultats nouveaux sur les processus gaussiens (
Gaussian processes)
Given a centered Gaussian process indexed by an arbitrary set~$T$, a major problem has been to find conditions implying that the sample functions are a.s. bounded, or a.s. continuous in the natural metric associated with the covariance. Here new necessary conditions for boundedness are given, which turn out to be sufficient in the case of stationary processes on $
R^n$. The conditions given here involve the existence of a majorizing measure, an idea which became crucial in the theory
Comment: For a systematic account of the theory around the time this paper was written, see Fernique's lectures in
École d'Été de Saint-Four~IV, LNM
480, 1974. For the definitive solution, see chapter 11 of Ledoux-Talagrand
Probability in Banach spaces, Springer 1991
Keywords: Gaussian processes,
Sample path regularityNature: Original
Retrieve article from Numdam
XII: 44, 567-690, LNM 649 (1978)
NANOPOULOS, Constantin;
NOBELIS, Photis
Régularité et propriétés limites des fonctions aléatoires (
Miscellanea,
Gaussian processes)
This paper extends to the non-Gaussian case methods to study the regularity of sample paths which have proved useful in the Gaussian case, notably that of majorizing measures (to be completed)
Comment: To be completed
Keywords: Sample path regularity,
Majorizing measuresNature: Original Retrieve article from Numdam
XII: 45, 691-706, LNM 649 (1978)
FERNIQUE, Xavier
Caractérisation de processus à trajectoires majorées ou continues (
Miscellanea,
Gaussian processes)
The methods which lead the author to necessary and sufficient conditions for boundedness or continuity of stationary Gaussian processes are extended and applied to non-stationary Gaussian processes and non-Gaussian processes
Keywords: Sample path regularityNature: Original Retrieve article from Numdam
XLV: 08, 201-244, LNM 2078 (2013)
CUCHIERO, Christa;
TEICHMANN, Josef
Path Properties and Regularity of Affine Processes on General State Spaces (
Theory of processes)
Keywords: affine processes,
path properties,
regularity,
Markov semimartingalesNature: Original
